Course 2

3-6 Solving Equations Containing Decimals

Do NowSolve.

1. x – 17 = 322. y + 11 = 41

3. = 18

4. 12x = 1085. x – 9 = 20

x = 49y = 30

w = 90

x = 9x = 29

w5

Hwk: p29 odd, Test this Friday on chap 3 sec 1-6.

Course 2

3-6 Solving Equations Containing Decimals

EQ: How do I solve one-step equations that contain decimals?

M7A2.a Given a problem, define a variable, write an equation, solve the equation, and interpret the solution;M7A2.b Use the addition and multiplication properties of equality to solve one- and two-step linear equations;M7N1.c Add, subtract, multiply, and divide positive and negative rational numbers; M7N1.d Solve problems usingrational numbers

Course 2

3-6 Solving Equations Containing Decimals

You can write an equation to represent this situation.The slowest time s minus 3.84 is equal to the fastesttime of 7.2 seconds.

s – 3.84 = 7.2

Students in a physical education class were running 40-yard dashes as part of a fitness test. The slowest time in the class was 3.84 seconds slower than the fastest time of 7.2 seconds.

Course 2

3-6 Solving Equations Containing Decimals

Solve.

Additional Example 1: Solving Equations by Adding and Subtracting

A. n – 2.75 = 8.3

n – 2.75 = 8.30+ 2.75 + 2.75

n = 11.05

Add to isolate n.

B. a + 32.66 = 42a + 32.66 = 42.00

–32.66 –32.66a = 9.34

Subtract to isolate a.

Course 2

3-6 Solving Equations Containing Decimals

Solve.

Check It Out: Example 1

A. n – 1.46 = 4.7

n – 1.46 = 4.70+ 1.46 + 1.46

n = 6.16

Add to isolate n.

B. a + 27.51 = 36a + 27.51 = 36.00

–27.51 –27.51a = 8.49

Subtract to isolate a.

Course 2

3-6 Solving Equations Containing Decimals

Solve.

Additional Example 2A: Solving Equations by Multiplying and Dividing

x4.8 = 5.4

x4.8

= 5.4

4.8x 4.8 =· 5.4 · 4.8 Multiply to isolate x.

x = 25.92

Course 2

3-6 Solving Equations Containing Decimals

Solve.

Additional Example 2B: Solving Equations by Multiplying and Dividing

9 = 3.6d

9 = 3.6d

93.6

3.69

2.5 = d

=3.6d3.6

= d

Divide to isolate d.

Think: 9 ÷ 3.6 = 90 ÷ 36

Course 2

3-6 Solving Equations Containing Decimals

Solve.

Check It Out: Example 2A

x3.5 = 2.4

x3.5

= 2.4

3.5x 3.5 =· 2.4 · 3.5 Multiply to isolate x.

x = 8.4

Course 2

3-6 Solving Equations Containing Decimals

Solve.

Check It Out: Example 2B

9 = 2.5d

9 = 2.5d

92.5

2.59

3.6 = d

=2.5d2.5

= d

Divide to isolate d.

Think: 9 ÷ 2.5 = 90 ÷ 25

Course 2

3-6 Solving Equations Containing Decimals

A board-game box is 2.5 inches tall. A toy store has shelving measuring 15 inches vertically in which to store the boxes. How many boxes can be stacked in the space?

List the important information:

• Each board-game box is 2.5 inches tall.

• The store has shelving space measuring 15 inches.

The total height of the boxes is equal to the height of one box times the number of boxes. Since you know how tall the shelf is you can write an equation with b being the number of boxes.

2.5b = 15

Course 2

3-6 Solving Equations Containing Decimals

Additional Example 3 Continued

2.5b = 15

2.5b = 152.5 2.5

b = 6

Six boxes can be stacked in the space.

Course 2

3-6 Solving Equations Containing Decimals

A canned good is 4.5 inches tall. A grocery store has shelving measuring 18 inches vertically in which to store the cans. How many cans can be stacked in the space?

List the important information:

4.5c = 18

Course 2

3-6 Solving Equations Containing Decimals

Check It Out: Example 3 Continued

Solve

4.5c = 18

4.5c = 184.5 4.5

c = 4

Four cans can be stacked in the space.

Course 2

3-6 Solving Equations Containing Decimals

You try on your paper, put name on paper

Solve.

1. x – 14.23 = 19.5

2. 12.6c = –103.32

3.

4. m + 12.97 =–14.35

5. The French Club is selling coupon books for $8.25 each. How many books must be sold to bring in $5,940?

c = –8.2

x = 33.73

x = 56.73x9.3

= 6.1

720 books

m = –27.32